Abstract
We analyze a multiple level-set method for solving elliptic Cauchy problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional based on TV-H1 penalization. Generalized minimizers for our Tikhonov functional are defined and an existence result is established. Moreover, convergence and stability results of the proposed Tikhonov method are derived. The proposed multiple level-set method is tested numerically, and our experiments demonstrate that the method is able to accurately recover multiple objects as well as multiple contrast levels.
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